Characterization of Shielding Efficiency for Power Electronics Frequency Domain ()
1. Introduction
Today new applications of power electronics systems appear in many domains like transport: more electric aircrafts or electric cars. In order to combine power and electronic systems in the same environment or to take into account normative constraints in term of electromagnetic field exposure for humans, electromagnetic compatibility (EMC) has to be integrated early in the design flow of the complete system (aircraft or car). The shielding is one of the most used solutions to avoid unwanted couplings between power systems and their environment. However, engineers have to identify the source of disturbance, its geometry and have to define the EMC constraints (for example the magnetic field at 8 cm in front of the converter [1]): what attenuation, what shielding in which material? Moreover, the solution must also satisfy others constraints like cost, weight, strength…
The sizing of a required shielding efficiency can be done analytically [2] in restricted cases: high frequency, far field and plane wave, 1D, homogenous, isotropic and single layer. The electromagnetic properties of the materials used have to be known. In the domain of power electronics, shielding must mitigate near fields coming from magnetic sources (strong currents with high variations) in the frequency range starting from a few kHz (chopping frequency) to 50 MHz (limit of the radiated emissions of a classical power electronics converter). In this specific case, analytical way is too limited to answer the industrial problematic.
Also, numerical analysis can be done to size a shielding in the frequency range of interest and for magnetic sources. However, a 3D Finite Element (FE) modeling is impossible to solve because of the number of unknowns due to the required mesh into the shielding to take into account the skin effect. A 2D approach is a good compromise between the number of unknowns and the reality of the modeled system. The only problem is then to know the properties of the materials used to inquire the numerical model. When new generations of materials are used (composite with inclusion of conducting nano material for example) a characterization phase is required to extract equivalent properties (permeability µ, conductiveity σ and permittivity ε).
For the frequency range of interest of power electronics devices (10 kHz to 50 MHz), there is no specific standard of experimental measurements to determine shielding efficiency [3-6]. So, a specific test bench has been developed to estimate the shielding efficiency in the context of power electronics.
This article describes the whole developed approach to solve the problematic of shielding in power electronics applications. First the analytical possibilities of sizing of shielding are described. This allows to have a canonical problem to validate the others approaches. Then, a 2D numerical modeling of shielding is described and a study of sensitivity of the size of the shielding under test compared to the diameter of the antennas is proposed. Finally, the sizing of the test bench is described; comparisons between analytical, 2D numerical and measurements results are made on different prototypes. New generation of materials (composite) and new associations of classical materials are then tested.
2. Context
In aeronautics, EMC problems are extremely important for the new generation “more electric” airplane, because the pneumatic and hydraulic actuators will be replaced by electrical ones (steering deflection, braking systems, landing gear…) in order to reduce the costs as well as the weight of the embedded systems. The use of electric materials in these systems, which have to take into account the constraints of aeronautical environments: vibrations, temperature, weight…, imposes reliability constraints and very strong restrictions in terms of EMC. Radiated emissions produced by such systems could create malfunctions in sensitive avionic surrounding equipments, in particular the embedded electronics.
In ground transport domain, two factors have given rise to new EMC problems: X-by-wire (drive-by-wire, fly-by-wire [7], break-by-wire [8] …) for sensitive and critical low level systems and hybrid or full electrical propulsion. Moreover, automotive manufacturers are concerned by constraints concerning the exposure of humans to electromagnetic fields.
To ensure a good functioning of critical low level systems and the security of persons near power electronics converters, normative constraints are imposed to manufacturers of systems or of vehicles [9]. These constraints can be “added” (i.e. take the maximum constraint for each frequency) giving specifications to meet. Starting from this specification (a maximum value of magnetic and/or electric field at a given place) and from the description of the electromagnetic source (geometry and electrical functioning) the shielding efficiency to meet can be expressed versus the frequency. Figure 1 shows an example of specification in term of shielding efficiency in the automotive domain. The H Field limit is specified in the interior of the vehicle in order to protect passengers and electronic equipments.
3. Analytical Sizing
The shielding efficiency is evaluated by the attenuation in dB. In this study, the attenuation is defined by the ratio of the field at a place inside an enclosed shielded room (noted s) divided by the field at the same place but without the shielded room (noted 0). This ratio can be calculated with the modulus of the global field or for a given spatial component. The attenuation can be defined in terms of electric or magnetic field (1, 2).
(1)
(2)
In this study, the distance between the source of perturbation and the observation point, the maximal frequency of interest and the nature of the source (strong current values with strong variations) lead to consider magnetic sources in a near field configuration. So, the H field and the AH attenuation will be considered for the entire study.
In [2] authors develop analytical formalism with some restrictions (
in which ω is the pulsation of the
Figure 1. Example of a specification concerning the H field limit in the interior of the vehicle.
wave) to describe the attenuation brought by a shielding. Different causes of attenuation are enlightened: reflection (3), and multiple reflections (5), transmission (4) and the nature of the source in near field (6).
The reflection losses are due to the discontinuity of the characteristic impedance of the propagation medium. The reflection losses are given by (3). At the interface air/ shielding, a part of the energy of the incident wave is reflected and the other part propagates through the shielding. The transmitted wave is submitted to an attenuation inside the shielding (transmission losses (4)) which depends on the skin depth δ. Finally, the wave arrives on the shielding/air interface where a new reflection occurs.
(3)
where Z0 is the characteristic impedance of free space (Z0 = µ0c0), 
is the characteristic impedance inside the shielding.
(4)
where t is the thickness of the shielding.
If the attenuation by transmission is low, multiple reflections inside the shielding can occur. In this case, a corrective term has to be added to AR and AA:AMR given by (5).
(5)
In our application domain, magnetic sources in near field are considered. In this case, AR must be replaced by (6):
(6)
where 
is the characteristic impedance of magnetic near field, r is the distance between the magnetic source and the shielding. Finally, the total attenuation is the sum of (4)-(6). Figure 2 shows an example for a 2 mm copper shielding, 10 mm from the source. Each phenomenon is represented by its attenuation and is plotted versus the frequency. The total attenuation is also plotted on Figure 2.
4. 2D Numerical Approach
To consolidate the analytical approach, a 2D axisymetric modelling was implemented in a commercial electromagnetic software (Flux) developed by CEDRAT. This software uses the Finite Element Method (FEM) with a magneto dynamic formulation. Specific boundary conditions were used (infinite box) on the external boundaries of the problem because the magnetic field is not conducted by a magnetic material like in a transformer. Also, the coils are modelled as copper conductors and the mesh is adapted to take into account the skin depth (referred to the maximal frequency of interest). This restriction will impact on the maximal frequency of the numerical results (2 MHz in the air and 100 kHz with a shielding).
A first simulation was run with two coils in air. One is supplied with 1 A noted I1 (modulus) and the current in the second coil (in short circuit) noted I2 (modulus) is then computed. The attenuation in air is computed by (7)
Figure 2. Different kinds of attenuations versus frequency for a 2 mm copper shielding 10 mm from the source.
for each frequency:
(7)
Figure 3 shows analytical results [10], numerical 2D axisymetric results and experimental results. The two coils have 15 mm radius, one turn, the diameter of the wire is 0.6 mm and the distance between the two coils is 22 mm. Figure 4 shows a numerical result.
Then the same problem was computed with a shielding inserted between the two coils. Special attention is paid to the mesh inside the shielding: it must be adapted to the skin depth i.e. two layers of triangular elements by δ (referred to the maximal frequency). The attenuation noted A, given by (8), is obtained by subtracting the attenuation without shielding Aair (7) to the attenuation with shielding Ashield Ashield is computed according to (8) considering I2shield (the current in the short circuited coil with the shielding) when I1 is kept constant.
(8)
(9)
Figure 5 shows results for a 50 µm aluminum shielding. The numerical approach was used to study the influence of different parameters: the width of the sample of shielding compared to the diameter of the coils, the influence of the distance between the source and the shielding, the number of turns of the coils, to verify the validity of the proposed shielding specifications (example of Figure 1)… These results are essential to realize the sizing of the test bench.
Figure 9 shows for different frequencies the leakage coupling between the two coils versus the ratio noted Rleakage: width of the perfect shielding divided by the diameter of the coils. Results of Figure 4 show that a minimal value of Rleakage = 4 must be respected. Other unwanted couplings between the two coils can exist (capacitive coupling in common mode for example) and are not take into account in the FE modeling (magnetodynamic formulation). In the next section, the modifications made on the test bench to avoid this phenomenon will be explained.
5. Experimental Characterization
All the developed approaches previously presented (analytical and 2D numerical) are not enough versatile to help engineers to size a shielding for a given application with specific constrains. Indeed, new composite materials or multilayer shielding associating conductors, magnetic and dielectric layers cannot be used because of the lack of information concerning their global shielding properties. So, an experimental test bench is required to extract global properties of different kinds of materials.
5.1. Experimental Test Bench
The main constrains for the developed test bench are:
• Frequency range: 20 kHz - 30 MHz.
• Size of samples under test: 200 × 200 mm.
• Magnetic source (low level to begin).
• Distance source/shielding: few cm.
• Large dynamic range: 80 dB (see Figure 1).
• All the mechanical part of the bench should be transparent for the EM waves in the frequency range of interest.
Figure 6 shows a representation of the test bench.